EP4430299A1

EP4430299A1 - Method and device of calibrating a yaw system of a wind turbine to reduce fatigue and increase power

Info

Publication number: EP4430299A1
Application number: EP22821446.6A
Authority: EP
Inventors: Thomas Esbensen; Jonas Weiss GUSTAVSEN; Maxence JOSSO
Original assignee: Siemens Gamesa Renewable Energy AS
Current assignee: Siemens Gamesa Renewable Energy AS
Priority date: 2021-12-23
Filing date: 2022-11-22
Publication date: 2024-09-18
Anticipated expiration: 2042-11-22
Also published as: CN118451251A; WO2023117252A1; EP4202205A1; EP4430299B1; US20250059955A1; ES3060967T3; DK4430299T3

Abstract

It is described a method of calibrating a yaw actuator of a wind turbine (1), comprising steps of performing an active yaw operation in a clockwise yaw direction and an active yaw operation in a counter-clockwise yaw direction; recording data of a wind direction and a power caused by both yaw operations, and averaging the data and calculating an error (Ecw + ccw) between an experimental power difference and a theoretical power difference of yaw operations in the clockwise direction and a counter-clockwise direction; determining a minimum (idx) of the error; and determining a yaw misalignment (γ ) based on the minimum error.

Description

DESCRIPTION

METHOD AND DEVICE OF CALIBRATING A YAW SYSTEM OF A WIND TURBINE TO REDUCE FATIGUE AND INCREASE POWER

Field of invention

The present invention relates to a method and device of calibrating a yaw system of a wind turbine.

It is important for a wind turbine to face the wind in order to maximize power production and minimize loads. The turbines are yawed based on a wind direction measurement, typically derived from a sensor atop a turbine nacelle, wherein the wind sensor can output a continuous signal indicative of the wind direction. If the wind direction measurement is just slightly off, it may result in a yaw misalignment which can cause a significant production loss and increased loading.

To ensure optimal performance of wind turbines, the controller settings (i.e., parameters of the wind turbine controller) need to be optimal. The influence of controller settings has a high impact on power production, loads, and acoustic noise emissions. It may be possible to improve the annual energy production of up to 1 to 2% by proper optimization, reduce structural loads significantly, and reduce noise emission.

Typically, a model of the wind turbine and/or models of the components of the wind turbine are used to derive controller settings. However, due to model limitations or simplifications of the wind turbine and/or the conditions (wind, terrain, environment, etc.) and deviations of the final product (production tolerances, calibration tolerances, etc.), the controller settings may have to be optimized in the field to ensure optimal performance of the wind turbines. EP 3225 837 A1 discloses a method for calibrating a wind di- rection measurement for a wind turbine. The method compris- ing: measuring plural samples of a relative wind direction representing a difference angle between a real wind direction and an orientation of a measurement equipment, in particular a direction orthogonal to a rotor blade plane, to obtain plu- ral measured relative wind directions; deriving a measured relative wind direction change based on the measured relative wind directions; measuring plural samples of a performance parameter indicating a performance of the wind turbine; de- riving a performance change based on the plural samples of the performance parameter; determining a correlation value between the measured relative wind direction change and the performance change; measuring further plural samples of the relative wind direction; and correcting the further measured relative wind directions based on the correlation value, to obtain corrected further measured relative wind directions. Summary of the Invention It is the object of the present invention to provide a method and a device of accurately calibrating a yaw system of a wind turbine, for example a wind direction sensor or a yaw actua- tor, to reduce fatigue and to increase power. This object may be achieved by the subject matters according to the independ- ent claims. The present invention is further developed as set forth in the dependent claims. According to a first aspect of the invention, a method of calibrating a yaw system of a wind turbine is provided. The wind turbine comprises a rotor having a plurality of rotor blades, each blade being configured to be pitched by a pitch angle about a pitch axis of the blade, the rotor being mount- ed to a nacelle to rotate about a rotation axis with a rotor speed to drive a generator for producing electrical energy, the nacelle being mounted to a tower to rotate about a yaw axis. The method comprises steps of: selecting a first prede- termined time span before a yaw operation and a second prede- termined time span after the yaw operation; performing a yaw operation in a clockwise yaw direction and a yaw operation in a counter-clockwise yaw direction; recording data of a wind direction and a performance parameter caused by both yaw op- erations, and averaging the data; determining a first experi- mental performance parameter in the first predetermined time span and a second experimental performance parameter in the second predetermined time span from the averaged data, pref- erably from the averaged data of the performance parameter, for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direction; calculating an experimental performance parameter difference between the first and second experimental performance parameters for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw di- rection; determining a first wind direction in the first pre- determined time span and a second wind direction in the sec- ond predetermined time span from the averaged data, prefera- bly from the averaged data of the wind direction, for each yaw operation in the clockwise yaw direction and the counter- clockwise yaw direction; calculating a first theoretical per- formance parameter in the first predetermined time span based on the determined first wind direction and a second theoreti- cal performance parameter in the second predetermined time span based on the determined second wind direction for each yaw operation in the clockwise yaw direction and the counter- clockwise yaw direction; calculating a theoretical perfor- mance parameter difference between the first and second theo- retical performance parameters for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direc- tion; calculating absolute errors between the experimental performance parameter difference and the theoretical perfor- mance parameter difference of the yaw operations in the clockwise direction and a counter-clockwise direction, re- spectively; adding the absolute errors of the yaw operations in the clockwise direction and the counter-clockwise direc- tion to obtain a total error; determining a minimum error of the total error; and determining a yaw misalignment based on the minimum error. In an embodiment, which is also referred as a hybrid mode which combines the active approach of the first aspect of the present invention with a passive approach, further comprises steps of: performing a yaw event at a yaw event time in the clockwise direction and the counter-clockwise direction; se- lecting a predetermined further time span directly before the yaw event time for each yaw event in the clockwise direction and the counter-clockwise direction; recording data of a wind direction and a performance parameter in the predetermined further time span before the yaw event time, and averaging the data for each yaw event in the clockwise direction and the counter-clockwise direction; determining a further first experimental performance parameter at the beginning of the further time span and a further second experimental perfor- mance parameter at the end of the further time span from the averaged data, preferably from the averaged data of the per- formance parameter, for each yaw event in the clockwise di- rection and the counter-clockwise direction; calculating a further experimental performance parameter difference between the further first and further second experimental performance parameters for each yaw event in the clockwise direction and the counter-clockwise direction; determining a further first wind direction at the beginning of the further time span and a further second wind direction at the end of the further time span from the averaged data, preferably from the aver- aged data of the wind direction, for each yaw event in the clockwise direction and the counter-clockwise direction; cal- culating a further first theoretical performance parameter at the beginning of the further time span based on the deter- mined further first wind direction and a further second theo- retical performance parameter at the end of the further time span based on the determined further second wind direction for each yaw event in the clockwise direction and the coun- ter-clockwise direction; calculating a further theoretical performance parameter difference between the further first and second theoretical performance parameters for each yaw event in the clockwise direction and the counter-clockwise direction; calculating further absolute errors between the further experimental performance parameter difference and the further theoretical performance parameter difference of the yaw events in the clockwise direction and the counter- clockwise direction, respectively; adding the absolute errors of the yaw events in the clockwise direction and the counter- clockwise direction to obtain a total error; determining a further minimum error of the further total error; and deter- mining a further yaw misalignment based on the further mini- mum error. Preferably, these steps are performed after the steps of the first aspect. In an embodiment, the yaw operation moves the nacelle in a range between -4° and +4°, preferably in a range between -3° and +3°, more preferred in a range between -2° and +2°. In an embodiment, averaging the data includes a filtering the data. In an embodiment, the predetermined time span is in a range between 30 and 240 s, preferably between 60 and 180 s. In an embodiment, the yaw misalignment is determined in a ma- trix which includes the error and the yaw misalignment for a range of wind direction offsets and yaw loss exponents. In an embodiment, the first wind direction is determined by use of a wind sensor, wherein sampled wind direction values are averaged at least in a part of the first predetermined time span; and/or the second wind direction is determined by use of a wind sensor, wherein sampled wind direction values are averaged at least in a part of the second predetermined time span. In an embodiment, the first theoretical performance parameter Pγ+WD2 is calculated as Pγ+WD2 = cos^∞(γ + WD2); and/or the second theoretical performance parameter Pγ+WD3 is calculated as ; wherein α is a yaw loss exponent and γ is the yaw misalignment. In an embodiment, the error is calculated as a sum of a first absolute error of the yaw operation in the clockwise yaw di- rection and a second absolute error of the yaw operation in the counter-clockwise yaw direction. In an embodiment, the performance parameter is selected from a group comprising a power-based parameter of an active elec- trical or mechanical output power of the wind turbine, and a wind speed-based parameter of an effective wind speed. The power-based parameter and the wind speed-based parameter can be or comprise a rotational speed of the rotor, an active electrical power produced by the generator, a collective pitch reference for collectively pitching all blades, given rotor performance data, operation states, etc. According to a second aspect of the invention, a device of calibrating a yaw system of a wind turbine is provided. The wind turbine comprises a rotor having a plurality of rotor blades, each blade being configured to be pitched by a pitch angle about a pitch axis of the blade, the rotor being mount- ed to a nacelle to rotate about a rotation axis with a rotor speed to drive a generator for producing electrical energy, the nacelle being mounted to a tower to rotate about a yaw axis. The device comprises a selecting unit for selecting a first predetermined time span before a yaw operation and a second predetermined time span after the yaw operation; a performing unit for performing a yaw operation in a clockwise yaw direction and a yaw operation in a counter-clockwise yaw direction; a recording unit for recording data of a wind di- rection and a performance parameter caused by both yaw opera- tions, and averaging the data; a first determining unit for determining a first experimental performance parameter in the first predetermined time span and a second experimental per- formance parameter in the second predetermined time span from the averaged data for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direction; a first calculating unit for calculating an experimental performance parameter difference between the first and second experi- mental performance parameters for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direc- tion; a second determining unit for determining a first wind direction in the first predetermined time span and a second wind direction in the second predetermined time span from the averaged data for each yaw operation in the clockwise yaw di- rection and the counter-clockwise yaw direction; a second calculating unit for calculating a first theoretical perfor- mance parameter in the first predetermined time span based on the determined first wind direction, and a second theoretical performance parameter in the second predetermined time span based on the determined second wind direction for each yaw operation in the clockwise yaw direction and the counter- clockwise yaw direction; a third calculating unit for calcu- lating a theoretical performance parameter difference between the first and second theoretical performance parameters for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direction; a fourth calculating unit for calculating absolute errors between the experimental per- formance parameter difference and the theoretical performance parameter difference of the yaw operations in the clockwise direction and a counter-clockwise direction, respectively; an adding unit configured to add the absolute errors of the yaw operations in the clockwise direction and the counter- clockwise direction to obtain a total error; a third deter- mining unit for determining a minimum error of the total er- ror; and a fourth determining unit for determining a yaw mis- alignment based on the minimum error. The utilization of data only before a yaw event eliminates possible errors and dynamics that may exist in a yaw control- ler, e.g., if a dead band or an offset error exist in a yaw control system, the resulting nacelle position might be in- correct. By eliminating uncertainties in the yaw control sys- tem possible errors used in the algorithm are also eliminat- ed. Advantageously, yaw errors can be reduced, the turbine power production (AEP) can be increased, turbine loads and fatigues can be decreased, and the nacelle can be aligned to the wind direction. The present invention does not require to poten- tially yaw the turbine out of the wind direction to estimate the offset. There is no additional cost for the customer. Offsets can be estimated using old data. Unpredictable behav- iours from wind sensors data obtained after operational yaws can be avoided so that the calibration is more accurate. It has to be noted that embodiments of the invention have been described with reference to different subject matters. In particular, some embodiments have been described with ref- erence to apparatus type claims whereas other embodiments have been described with reference to method type claims. However, a person skilled in the art will gather from the above and the following description that, unless other noti- fied, in addition to any combination of features belonging to one type of subject matter also any combination between fea- tures relating to different subject matters, in particular between features of the apparatus type claims and features of the method type claims is considered as to be disclosed with this application. Brief Description of the Drawings The aspects defined above and further aspects of the present invention are apparent from the examples of embodiment to be described hereinafter and are explained with reference to the examples of embodiment. The invention will be described in more detail hereinafter with reference to examples of embodi- ment but to which the invention is not limited. Fig. 1 shows a wind turbine and the different elements thereof according to an embodiment; Fig. 2 shows a top view of a nacelle of a wind turbine according to an embodiment; Fig. 3 shows a definition of a yaw direction according to an embodiment; Fig. 4 shows a top view of a nacelle of a wind turbine and defines different angles according to an em- bodiment; Fig. 5 shows recorded data of a wind direction and a na- celle position in a predetermined time span be- fore a yaw event in the clockwise direction ac- cording to an embodiment; Fig. 6 shows recorded data of a filtered yaw error and a power in the predetermined time span before the yaw event in the clockwise direction according to an embodiment; Fig. 7 shows averaged data of a wind direction and a na- celle position in the predetermined time span be- fore the yaw event in the clockwise direction ac- cording to an embodiment; Fig. 8 shows averaged data of the filtered yaw error and the power in the predetermined time span before the yaw event in the clockwise direction accord- ing to an embodiment; Fig. 9 shows averaged data of a wind direction and a na- celle position in the predetermined time span be- fore the yaw event in the counter-clockwise di- rection according to an embodiment; Fig. 10 shows averaged data of the filtered yaw error and the power in the predetermined time span before the yaw event in the counter-clockwise direction according to an embodiment; Fig. 11 shows power levels read from the averaged power time trajectory according to an embodiment; Fig. 12 shows averaged data of a wind direction in the predetermined time span before the yaw event in the clockwise direction measured by a primary and a secondary anemometer according to an embodi- ment; Fig. 13 shows averaged data of a wind direction in the predetermined time span before the yaw event in the counter-clockwise direction measured by the primary and the secondary anemometer according to an embodiment; Fig. 14 shows averaged data of a wind direction in the predetermined time span before the yaw event in the counter-clockwise direction measured by a primary and a secondary anemometer according to an embodiment; Fig. 15 shows theoretical power losses for different yaw loss exponents according to an embodiment; Fig. 16 shows the theoretical power losses for starting a yaw event in the clockwise direction and the counter-clockwise direction according to an em- bodiment; Fig. 17 shows a wind direction signal during a yaw opera- tion according to an embodiment; Fig. 18 shows offset results during a yaw operation in an adaptation mode according to an embodiment; Fig. 19 shows signals of a wind direction and a nacelle position during a yaw operation in the clockwise direction according to an embodiment; Fig. 20 shows signals of a filtered yaw error and power time trajectory during a yaw operation in the clockwise direction according to an embodiment; Fig. 21 shows signals of a wind direction and a nacelle position during a yaw operation in the counter- clockwise direction according to an embodiment; Fig. 22 shows signals of a filtered yaw error and power time trajectory during a yaw operation in the counter-clockwise direction according to an em- bodiment; Fig. 23 shows power levels read from a power curve during a yaw operation in the clockwise direction ac- cording to an embodiment; Fig. 24 shows power levels read from a power curve during a yaw operation in the counter-clockwise direc- tion according to an embodiment; Fig. 25 shows signals of a wind direction read from a wind direction curve during a yaw operation in the clockwise direction according to an embodi- ment; and Fig. 26 shows signals of a wind direction read from a wind direction curve during a yaw operation in the counter-clockwise direction according to an embodiment. Detailed Description The illustrations in the drawings are schematically. It is noted that in different figures, similar or identical ele- ments are provided with the same reference signs. Fig. 1 shows a wind turbine 1. The wind turbine 1 comprises a nacelle 3 and a tower 2. The nacelle 3 is mounted at the top of the tower 2. The nacelle 3 is mounted rotatable with re- gard to the tower 2 by means of a yaw bearing. The axis of rotation of the nacelle 3 with regard to the tower 2 is re- ferred to as the yaw axis 9. The wind turbine 1 also comprises a rotor 4 with three rotor blades 6 (of which two rotor blades 6 are depicted in Fig. 1). The rotor 4 is mounted rotatable with regard to the na- celle 3 by means of a main bearing 7. The rotor 4 is mounted rotatable about a rotation axis 8 (rotor axis). The wind turbine 1 furthermore comprises a generator 5. The generator 5 in turn comprises a rotor connecting the genera- tor 5 with the rotor 4. If the rotor 4 is connected directly to the generator 5, the wind turbine 1 is referred to as a gearless, direct-driven wind turbine. Such a generator 5 is referred as direct drive generator 5. As an alternative, the rotor 4 may also be connected to the generator 5 via a gear box. This type of wind turbine 1 is referred to as a geared wind turbine. The present invention is suitable for both types of wind turbines 1. The generator 5 is accommodated within the nacelle 3. The generator 5 is arranged and prepared for converting the rota- tional energy from the rotor 4 into electrical energy in the shape of an AC power. Fig. 2 shows a top view of a nacelle 3 of a wind turbine 1 according to an embodiment. The wind direction W varies al- most continuous and therefore it is desired to adjust the di- rection of the nacelle 3, which coincides with the rotation axis 8, to ensure that the nacelle 3 is facing the wind. Due to limited yaw capacity, the nacelle 3 can be misaligned to the wind direction; the wind turbine may only be yawing 5 to 10 % of the time. Typically, a certain yaw error is required before the yaw system is activated. A yaw error of approxi- mately 3 to 4° is required for initiating yawing, i.e., a yaw event. This is the dead band of a yaw controller. This means that the wind direction W changes of up to six degrees can occur without the yaw system being activated. Such a change is large enough to affect the performance of the turbine 1. Furthermore, the yaw error evaluated for yaw control can be filtered (averaged/made slower) such that instantaneous yaw errors for a short time exist which are much higher. When the wind direction W overcomes this threshold of the dead band and the nacelle 3 yaws to face the wind, this is defined as an operational yaw event. Fig. 3 shows definitions of yaw directions in clockwise and counter-clockwise directions according to an embodiment. The method considers changes in the wind direction leading up to a yaw event in both clockwise (CW) and counter-clockwise (CCW) direction. The definition can be seen in Fig. 2 where the nacelle 3 is illustrated seen from above. Reference sign W designates the relative wind direction and reference sign 8 is the rotation axis which coincides with the actual nacelle orientation. Fig. 4 shows a top view of a nacelle 3 of a wind turbine 1 and defines different angles according to an embodiment. The aim of the yaw controller is to align the nacelle 3 with a required offset. The offset is generally 0° but in specific cases, the user or wind farm operator may not want the na- celle 3 precisely aligned with the wind direction. The defi- nitions can be seen in Fig. 3 as follows: The yaw misalignment [deg] is the difference between the na- celle orientation, i.e., the rotation axis 8, and the wind direction Wvector (in the shape of a vector) relative to the cardinal point NORTH. When defined in terms of quantities specified relative to NORTH, the following definitions are valid: The nacelle position [deg] is an angle between NORTH and the rotation axis 8. The yaw offset is a desired yaw misalignment (i.e., the set- point/reference signal for the yaw misalignment). The yaw er- ror is a control error in the yaw system, defined by the dif- ference between the current nacelle position and the desired nacelle orientation. The yaw error can also be defined in terms of the previous two definitions yaw error = yaw Offset – yaw misalignment [deg]. When no yaw offset is applied, the definition becomes: yaw error = −yaw misalignment [deg]. The method of calibrating a yaw system of the wind turbine 1 comprises a step of performing a yaw event at a yaw event time T0 in a clockwise direction and a counter-clockwise di- rection as described with respect to Fig. 2. Furthermore, a predetermined time span directly before the yaw event time T0 is selected for each yaw event in the clockwise direction and a counter-clockwise direction. The time span can be in a range between 30 and 240 s, preferably between 60 and 180 s. In the present embodiments, the time span is selected to be 120 s. Findings suggest for example at least 800 yaw events or samples, which are approximately equal to 11 days. The method of calibrating a yaw system of the wind turbine 1 comprises a step of recording data of a wind direction and a power as an example of the performance parameter in the pre- determined time span before the yaw event time T0, as de- scribed with reference to Figures 5 and 6. Fig. 5 shows recorded data of a wind direction and a nacelle position in the predetermined time span before a yaw event in the clockwise direction according to an embodiment, and Fig. 6 shows recorded data of a filtered yaw error and a power in the predetermined time span before the yaw event in the clockwise direction according to an embodiment. In the present invention, it is desired to construct an aver- aged trajectory of considered signals which will be used to determine the general behavior of a turbine 1 for a given time period. The averaged trajectory represents the general behavior of the performance measures (wind direction and pow- er). For example, in a given time range (e.g., 3 weeks), rel- evant situations are identified, and time shifted to center yaw events and finally averaged all situations to a single data series which reflects the plurality of events. The steps are elaborated in the following. In the filtering step, it is desired to isolate the yaw events where the turbine 1 performs a normal operation mode, and to disregard special instances (e.g., startup). Such a filter can consider a normal operation, an underrated power, minimum power above a threshold (e.g., 100 kw), no curtail- ment, etc. In addition to that, yaw events can be filtered out where no other yaw events occur within a time window before 120 s. Also, the data are grouped in CW and CCW directions. In a resetting step, time stamps for all situations are reset such that when the wind direction drifts off and the yaw con- troller activates, this can be considered as the start of the yaw event. If the time trajectory is chosen to be 120 s be- fore the yaw event and 120 s after the yaw event, the results can be seen in figures 5 and 6, where 10 timeseries have been put on top of each other for CW (clockwise) yaw events. The power curves have been normalized (for example with reference to a power at the beginning of the time span). The method of calibrating a yaw system of the wind turbine 1 comprises a step of averaging the data for each yaw event in the clockwise direction and a counter-clockwise direction, as described with reference to Figures 7 to 10. In the step of averaging, when the power signal has been normalized and a bias has been removed for the nacelle position, all signals are averaged for each time step to produce a single timeseries that represents the behavior of the wind turbine 1 for the given time period. As a result, the averaged trajectories are depicted in Fig- ures 7 to 10. The vertical line symbolizes the yaw event at the yaw event time T0. Averaged trajectories for CW (clock- wise) and CCW (counter-clockwise) for the wind turbine 1 can be seen. Fig. 7 shows averaged data of a wind direction and a nacelle position in the predetermined time span before the yaw event in the clockwise direction according to an embodiment, Fig. 8 shows averaged data of the filtered yaw error and the power in the predetermined time span before the yaw event in the clockwise direction according to an embodiment, Fig. 9 shows averaged data of a wind direction and a nacelle position in the predetermined time span before the yaw event in the coun- ter-clockwise direction according to an embodiment, and Fig. 10 shows averaged data of the filtered yaw error and the pow- er in the predetermined time span before the yaw event in the counter-clockwise direction according to an embodiment. The method of calibrating a yaw system of the wind turbine 1 further comprises a step of determining a first experimental power P1 at the beginning of the time span and a second ex- perimental power P2 at the end of the time span from the av- eraged data for each yaw event in the clockwise direction and a counter-clockwise direction. For example, the first experi- mental power P1 at the beginning of the time span is the pow- er at t = 0 s in the lower picture in Fig. 10, and the second experimental power P2 at the end of the time span is the pow- er at t = 120 s in the lower picture in Fig. 10. The method of calibrating a yaw system of the wind turbine 1 comprises a step of calculating an experimental power differ- ence P2 - P1 between the averaged first and second experi- mental powers P1, P2 for each yaw event in the clockwise di- rection and a counter-clockwise direction. As shown in Figures 7 and 8, a recovery (after the yaw) of power, nacelle position, and filtered yaw error does not match with the wind direction from the anemometer. The fig- ures show the wind direction in normal production surrounded by operational yaw event. It is observed that the yaw event is triggered due to an increasing yaw misalignment of the na- celle up to 15 [deg]. The wind turbine action is a change in the nacelle position of 2.5 [deg]. It is expected that the wind direction and nacelle position should recover equally (change in the nacelle position should be equal to the yaw misalignment.) However, there are unexplainable behaviors of wind direction data after operational yaws. The wind direc- tion and the nacelle position does not recover equally, so that wind data after the yaw can be unreliable. The present invention overcomes this flaw. Fig. 11 shows power levels read from the averaged power time trajectory according to an embodiment, e.g., the averaged power trajectory for a CCW event similar to the bottom pic- ture in Fig. 10, where the yaw event occurs at 120 s. The normalized power output values of P1 and P2 is determined. P1 can be determined by making a mean of the values from 0 s to 40 s: P1_1:20 = 1.03 P2 could be a mean of the values collected 40 s before the yaw event and up to the yaw event: P2_(120-10:120) = 0.98 The change in power is found and used for further procession: ΔP_CCW = P₂ – P₁ = 0.98 − 1.03 = −0.05 The method of calibrating a yaw system of the wind turbine 1 further comprises a step of determining a first wind direc- tion WD1 at the beginning of the time span and a second wind direction WD2 at the end of the time span from the averaged data for each yaw event in the clockwise direction and a counter-clockwise direction, and of calculating a first theo- retical power Pγ+WD1 at the beginning of the time span based on the determined first wind direction WD1 and a second theo- retical power Pγ+WD2 at the end of the time span, based on the determined second wind direction WD2 for each yaw event in the clockwise direction and a counter-clockwise direction, as described in the embodiment of Figures 12 to 16. Fig. 12 shows averaged data of a wind direction in the prede- termined time span before the yaw event in the clockwise di- rection measured by a primary and a secondary anemometer ac- cording to an embodiment; Fig. 13 shows averaged data of a wind direction in the predetermined time span before the yaw event in the counter-clockwise direction measured by the pri- mary and the secondary anemometer according to an embodiment; and Fig. 14 again shows averaged data of a wind direction in the predetermined time span before the yaw event in the coun- ter-clockwise direction measured by the primary and the sec- ondary anemometer according to an embodiment. According to the background of the present invention, a pas- sive approach is applied, where a regular yaw event is used (meaning yaw events that occur because the wind is changing), and the nacelle 3 is tracking the wind direction (by the yaw controller). This is contrary to a smart yaw operation, where an offset is actively added on top of the wind direction sen- sor to increase or decrease the yaw misalignment. The perfor- mance data is compared before and after the added offset to determine if the yaw misalignment is either positive or nega- tive (CW or CCW). After a certain number of decisions (e.g. 100), a small offset/step (e.g. 0.3 deg) is then applied to the current offset. An AWDC-method (Automatic-Wind-Direction Calibration, based on data prior to a yaw event) requires a certain amount of collected data in order to compute an off- set. Roughly estimates are point towards a least 800 passive yaws. Advantages of this method are that it is possible to exclude dynamics, and yaw misalignment that may exists in the yaw controller. Furthermore, this method differs from prior knowledge as it does not require data after the yaw event and hereby avoid introducing inaccuracies in sensors (anemome- ters) and unexplainable behavior in the wind sensor (anemome- ter) at and after the yaw event. Next, the behaviors of the wind direction sensors are de- scribed. As described before, the exact value of the wind di- rection is difficult to assess. When considering the behavior before the yaw event, the wind can attain the following de- velopment: - Exponential behavior of the primary sensor, - Exponential behavior of the secondary sensor, - Linear behavior of wind direction. The exponential behavior of the primary and secondary sensors can be seen in Figures 7 to 10. One can chose either of the wind direction behaviors depending on what is considered best for the given situation. In general, results have shown that both the primary and secondary exponential behaviors give good results and that the linear behavior is mostly off. Fig. 12 particularly shows an example of different exponen- tial behaviors of a primary sensor and a secondary sensor, and Fig. 13 particularly shows an example of a linear behav- ior on the secondary sensor. It is to be noted that based on previous investigations, the sensor data just before the yaw event on the primary sensor is believed to be misleading, therefore the data of the pri- mary sensor can be clipped at 10°. The three possible devel- opments for the wind direction can be seen in Fig. 14. The value of the reference wind direction WD1 before the yaw event can either be: 1.a Average of the first 15 seconds of the primary sensor, if exponential behavior, or linear behavior is chosen. 1.b Average of the first 15 seconds of the secondary sensor if exponential behavior. The value of the wind direction just before the yaw event WD2 can either be: 2.a Last 10 seconds before the yaw event of the primary sen- sor, clipped at 10° if exponential behavior is chosen. 2.b Last 10 seconds before the yaw event of the secondary sensor, clipped at 10° if exponential behavior is chosen. 2.c A linear interpolation of the primary sensor data based on the average power of t = [0:15]s and of t = [45:55]s, if linear behavior is chosen. Assuming an exponential wind direction development and uti- lizing the primary wind direction sensor, the averaged data are clipped at 10 [deg] for the CW direction in Fig. 14: WD1_0:15 = 4° WD2_(120-10):120 = 10° Fig. 15 shows theoretical power losses for different yaw loss exponents according to an embodiment; and Fig. 16 shows the theoretical power losses for starting a yaw event in the clockwise direction and the counter-clockwise direction ac- cording to an embodiment. The theoretical power may be expressed in terms of a model e.g., as a relationship indicated by the equation below and seen in Fig. 15: where γ is the yaw misalignment, α is the yaw loss exponent, P_γ is the power with a misalignment γ, and P₀ is the power without any yaw misalignment. The exact value of the yaw loss exponent can be determined in a conventional manner (see Jaime Liew, Albert M. Urbán, and Søren Juhl Andersen, “Analytical model for the power–yaw sen- sitivity of wind turbines operating in full wake”, Wind Ener- gy Science, 31 March 2020). The power losses for different yaw loss exponents can be seen in Fig. 16. In the following is it assumed that the P₀ = cos^∞(0°) = 1 therefore it is assumed that P_γ = cos^∞(γ). This equation can be for the locations from the averaged trajectories (before the yaw event and just before the yaw event). Pγ+WD1 = cos^∞(γ+WD1) and Pγ+WD2 = cos^∞(γ+WD2) The method of calibrating a yaw system of a wind turbine 1 further comprises a step of calculating a theoretical power difference Pγ+WD1 - Pγ+WD2 between the first and second theo- retical powers Pγ+WD1, Pγ+WD2 for each yaw event in the clockwise direction and a counter-clockwise direction with reference to the embodiment of Figures 15 and 16. Combining the equations yields the theoretical power difference: ΔP = Pγ+WD1 - Pγ+WD2 = cos^∞(γ+WD1) - cos^∞(γ+WD2) Fig. 16 shows that for a given offset in the CCW direction, a large power loss is expected whereas in the CW direction the power is supposed to remain relatively stable. If the offset was -10°, the CCW movement would lead to a larger power loss and the CW change would lead to a power gain, as seen on the example averaged power time trajectories Figures 7 to 10. For example, the theoretical power changes when varying the yaw misalignment γ [-20:20] and the yaw loss exponent Į [1.4; 1.7; 2.2] in the CW direction: ΔP_CW = cos^∞(γ + 4°) − cos^∞(γ + 10°) The same is done for the CCW direction: ΔP_CCW = cos^∞ (γ + WD1_CCW) − cos^∞ (γ + WD1_CCW) The method of calibrating a yaw system of a wind turbine 1 further comprises a step of calculating an absolute error (Ecw + Eccw) between the experimental power difference (P2 - P1) and the theoretical power difference (Pγ+WD1 - Pγ+WD2) of the yaw events in the clockwise direction and a counter- clockwise direction, for example like: Ecw + Eccw = abs(ΔP_theoryCW - ΔP_expCW) + abs(ΔP_theoryCCW - ΔP_expCCW) = abs((Pγ+WD1 - Pγ+WD2)_CW - (P2 - P1)_CW) + abs((Pγ+WD1 - Pγ+WD2)_CCW - (P2 - P1)_CCW). The method of calibrating a yaw system of a wind turbine 1 further comprises a step of determining a minimum error, and eventually determining a yaw misalignment based on the mini- mum error. For example, the minimum error in the matrix of errors can be determined like: error = min(Ecw + Eccw) This error corresponds to a specific yaw error offset which is the wind direction deviation. By adjusting the found yaw error offset to the yaw control- ler, the performance measure should increase. The description above refers to a passive approach, where a yaw event is triggered when a yaw error exceeds a predeter- mined angle. The yaw error is estimated based on data ob- tained before the yaw event. The description below refers to an active approach according to the present invention, where a yaw operation is actively performed in a clockwise yaw direction and in a counter- clockwise yaw direction, and data of a wind direction and a power as a performance parameter caused by both yaw opera- tions are recorded and averaged, after having selected a first predetermined time span before the active measurement yaw and a second predetermined time span after the active yaw. Here, the yaw error is estimated based on data before and afterwards the active yaw. Contrary to the embodiments described above, the following embodiments utilize an active yaw operation to extract data for further processing. In oth- er words, the algorithm makes the turbine actively yaw fourth and back to determine if any of the yaw operations leads to an increase or decrease in performance measure. In the following embodiments, the wind direction becomes more predictable. Thereby, is it possible to trust and use the wind sensors and the equivalent data. Also, because the sig- nal remains more stable, is it possible to average the power and the wind direction over a longer time span and thereby obtain a more accurate result. In a suggested new hybrid approach, the passive and the ac- tive methods can be combined, i.e., after the active approach performing the active yaw, the passive approach analyzing the yaw event can be performed. Thereby, the movement of the is used to acquire data, and afterwards, the passive analysis is performed on top. This hybrid method offers a more trustworthy and more stable wind direction measurements and estimates a finite value for the offset instead of only the offset direction (+/-), this method would not need to move far out of the actual wind di- rection as done in a pure SmartYaw mode (+4°/-4°) because a range of only ±2° or ±3° is sufficient. With enough data, the power curves would be constant before and after the yaw oper- ation (like in smart yaw), and the wind direction can pre- cisely be estimated. Once the data is collected, a passive analysis can be performed, and the offset should be precisely estimated. The hybrid method can be utilized in two different ways: 1. Recalibrating sensors when the turbine is installed; 2. Validating/Adjusting an offset found by SmartYaw due to changes (environment, sensor drift off and the like.) The basic idea of the passive analysis is to compare experi- mental power changes and wind direction changes with theoret- ical changes. However, in situations with active yawing, the wind direction changes much less and seems more predictable compared with results which are acquired in a yaw event (fol- lowing the wind direction drifting), meaning that the theo- retical power estimations are more precise. The inventors carried out tests, where active yawing was ac- tive and the wind direction switched from approximately -4° to approximately +4°. It is worth noting that in this situa- tion, active yawing is supposed to have corrected the offset, so the power levels are expected to be identical when the wind direction is at -4° and +4°. The events for a yaw opera- tion in the clockwise direction can be separated into three regions: 1. The yaw misalignment is around -4°. 2. When going from negative offset to a positive offset, an offset of +8° is added on the wind direction signal. The pas- sive yaw controller will try to compensate for the error to realign with the wind direction. 3. The yaw misalignment is around +4°. These three steps are reflected in the wind direction signal in Fig. 17 which shows a wind direction signal during such active yaws according to an embodiment. In selecting the first predetermined time span before the yaw operation and the second predetermined time span after the yaw operation, it is worth noting that the results can be heavily impacted by the number of yaw operations that go through a filtering step. With less than 500 yaw operations, the averaging of the normalized power curve can lead to mis- leading results. It is worth mentioning that, when active yawing is in adaptation mode, the offset will change with time. In order to utilize the passive analysis, the chosen data must have an offset which is constant, the moving offset has not yet been coded and implemented as a part of the pas- sive offset estimation. For example, Fig. 18 shows offset results during a yaw opera- tion in an adaptation mode according to an embodiment. The offset moves up until the 20th of August but stays in the same region afterwards. The passive analysis will then be tested between 20/08/2020 and 29/08/2020, which are 9 days and correspond to approximately 400 situations. For the selected time spans, the average trajectory technic is applied to construct the average trajectories. Fig. 19 shows signals of a wind direction and a nacelle posi- tion during an active yaw in the clockwise direction accord- ing to an embodiment; Fig. 20 shows signals of a filtered yaw error and power time trajectory during active yawing in the clockwise direction according to an embodiment; Fig. 21 shows signals of a wind direction and a nacelle position during ac- tive yawing in the counter-clockwise direction according to an embodiment; and Fig. 22 shows signals of a filtered yaw error and power time trajectory during an active yaw in the counter-clockwise direction according to an embodiment. A first experimental power P2 in the first predetermined time span and a second experimental power P3 in the second prede- termined time span are determined from the recorded data for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direction. Fig. 23 shows power levels read from a power curve during an active yaw in the clockwise direction according to an embodi- ment. In determining the experimental changes in performance measure, normalized power output values of P2 and P3 are de- termined in the clockwise direction (and the counter- clockwise direction, respectively). For example, P2 can be determined by making a mean of the values from 0 s to 120 s. T0 = time for active yaw (120s) P2_CW(0:120) = 1.0. (0:T0) For example, P3 could be a mean of the values collected 60 s after the yaw operation and until the end. It takes approxi- mately 6 s or more for the power and wind direction to settle after a yaw. P3_{CW(120+60:240)} = 0.995 (T0+60:end) The change in power is found and used for further processing: ΔP_CW = P3_CW − P2_CW = 0.995 − 1.0 = −0.005 Fig. 24 shows power levels read from a power curve during an active yaw in the counter-clockwise direction according to an embodiment. For example, P2 and P3 can be determined as fol- lows: P2_CCW(0:120) = 1.00 P3_{CCW(120+60:240)} = 1.01 Then, an experimental power difference P3 – P2 between the first and second experimental powers P2, P3 for each in the clockwise yaw direction and the counter-clockwise yaw direc- tion is calculated. For example, the change in power can be determined as follows: ΔP_CCW = P3_CCW − P2_CCW = 1.01 − 1.00 = 0.01 The same for the wind direction. Next, a wind direction WD2 in the first predetermined time span and a secondary wind direction WD3 in the second prede- termined time span from the recorded data for the averaged trajectory in the clockwise yaw direction and the counter- clockwise yaw direction are determined. Fig. 25 shows wind direction during an active yaw in the clockwise direction according to an embodiment; and Fig. 26 shows wind direction during an active yaw in the counter- clockwise direction according to an embodiment. Here, wind direction values of WD2 and WD3 are determined in the clock- wise and counter-clockwise directions. For example, in the clockwise direction with regards to Fig. 25, WD2 can be determined by making a mean of the values from 0 s to 120 s: WD2_CW(0:120) = 0.4°, T0 = active yaw WD3 could be a mean of the values collected 60 s after the yaw operation and until the end: WD3_{CW(120+60:240)} = −0.6° For example, in the counter-clockwise direction with regards to Fig. 26, WD2 and WD3 can be calculated as follows: WD2_CCW(0:120) = −0.1° WD3_{CCW(120+60:240)} = −0.1° Thereafter, for a range of offsets γ and for a specified yaw loss exponent Į, a theoretical power Pγ+WD2 in the first pre- determined time span based on the determined first wind di- rection WD2. A theoretical power Pγ+WD3 in the second predetermined time is calculated based on the determined second wind direction WD3 utilizing the averaged trajectory in both the clockwise yaw direction and the counter-clockwise yaw direction. For example, the theoretical power changes can be calculated when varying the yaw misalignment γ [-20:100:20] and the yaw loss exponent Į [1.4; 1.7; 2.2] using the theoretical equa- tions presented before: ΔP = cos^∞(γ + WD3) − cos^∞(γ + WD2) Applied in the clockwise direction: ΔP_CW = cos^∞(γ + (−0.6°)) − cos^∞(γ + 0.4°) Applied in the counter-clockwise direction: ΔP_CCW = cos^∞(γ + (−0.1°)) − cos^∞(γ + (−0.1°)) The resulting values can lead to a matrix containing the er- ror related to various yaw misalignment and various yaw loss exponent, for example with the dimensions [3x100]. 100 repre- sents a number of combinations of a yaw misalignment and yaw loss exponent and corresponding resulting error. Then, a power error (Ecw + Eccw) between the experimental power difference and the theoretical power difference of the averaged trajectory in the clockwise direction and a counter- clockwise direction is calculated. For example, the absolute error is used as the power can both increase or decrease: E_CW+CCW = abs(ΔP_TheoryCW – ΔP_ExpCW) + abs(ΔP_TheoryCCW − ΔP_ExpCCW) E_CW+CCW = abs((cos^∞(γ − 0.6°) − cos^∞(γ + 0.4°)) − (−0.005)) + abs((cos^∞(γ − 0.1°) − cos^∞(γ − 0.1°)) − 0.01) Then, a minimum index (idx) of the error is determined, i.e., the minimum error in the matrix of performance measure errors is identify the related yaw misalignment and yaw loss expo- nent. index = min(E_CW+CCW) Thereafter, the yaw misalignment is determined based on the minimum error. yaw misalignment γ can be looked-up from the matrix [3x100], by getting the offset and yaw loss exponent corresponding to the minimum error: γ = E_CW+CCW(idx) By this embodiment, a yaw offset can accurately be derived. By adjusting a yaw error offset to the yaw controller, the yaw misalignment error can be found. The active yawing can be applied “on the fly” and uses less data than the passive approach. For example, the passive ap- proach usually needs data of more than one day. Even when the offset has been stabilized by active yawing, the number of yaw operations that can be used is still quite small. The switching of the yaw misalignment between -4° and 4° can have an impact on the energy production during the adaptation mode. The passive approach can be applied without imposing any yaw misalignment. The hybrid method could require a smaller yaw misalignment, for example between ±2 and ±3°. The precision of active yawing and the hybrid method is bet- ter than the passive approach since the wind direction will be better known. In the hybrid approach, the wind direction is more stable so the averaging can be done on a longer peri- od of time, thus leading to more accurate results. Advanta- geously, the hybrid approach utilizes the benefits of active yawing (stable wind direction) and performs the passive ap- proach on top to compute an exact offset instead of just a direction. Hence, the method is more accurate, the AEP (Annu- al Energy Production) can be increased, and fatigues and tur- bine loads are reduced. Any turbine can quickly be recali- brated (for example within one day) so that a downtime is minimized. The minimization of yaw errors will result in more correct inputs for park features like wake-adapt and north- calibration. The performance parameter is not limited to the power but can be any power-based parameter which reflects an active elec- trical or mechanical output power of the wind turbine 1. The performance parameter can be a wind speed-based parameter of an effective wind speed, i.e., a wind speed component par- allel to the nacelle 3, which can provide a consistent meas- ure of the turbine performance at all wind speeds. This pa- rameter can be estimated from turbine models, the actual pow- er production, the actual rotor speed, and the actual pitch angle. This is possible as all possible combinations of wind speed, rotor speed, and pitch angle will result in a theoret- ical power output, and thus the effective wind speed can be estimated if the actual operational values are known. If the estimated effective wind speed is derived from the ro- tational speed, active electrical power, pitch angle and mod- el data, this measure reflects the underlying, or “true”, mo- mentary energy available in the incoming wind and turbine system, and thus has the inherent advantage of being continu- ous up to and above the maximum rated power of the turbine, which is otherwise saturated at some upper level due to phys- ical limitations in, e.g., the generator and other mechanical components. With reference to Figures 15 and 16, the relation P_γ = cos^∞(γ) * P₀ holds where γ is the yaw misalignment, ^ is the yaw loss ex- ponent, ^γ is the power with a misalignment γ, and ^0 is the power without any yaw misalignment. A similar relation holds for the effective wind speed W, i.e., W_Ȗ = cos^∞(γ) * W₀ where γ is the yaw misalignment, ^ is the yaw loss exponent, Wγ is the effective wind speed with a misalignment γ, and W0 is the effective wind speed without any yaw misalignment. However, the yaw loss exponent Į for the effective wind speed might be different from the yaw loss exponent Į of the power. It should be noted that the term “comprising” does not ex- clude other elements or steps and “a” or “an” does not ex- clude a plurality. Also elements described in association with different embodiments may be combined. It should also be noted that reference signs in the claims should not be con- ^{strued as limiting the scope of the claims.}

Claims

CLAIMS 1. A method of calibrating a yaw system of a wind turbine, the wind turbine (1) comprising a rotor (4) having a plurali- ty of rotor blades (6), each blade (6) being configured to be pitched by a pitch angle about a pitch axis of the blade (6), the rotor (4) being mounted to a nacelle (3) to rotate about a rotation axis (8) with a rotor speed to drive a generator (5) for producing electrical energy, the nacelle (3) being mounted to a tower (2) to rotate about a yaw axis (9), the method comprising steps of: selecting a first predetermined time span before a yaw operation and a second predetermined time span after the yaw operation; performing a yaw operation in a clockwise yaw direction and a yaw operation in a counter-clockwise yaw direction; recording data of a wind direction and a performance pa- rameter caused by both yaw operations, and averaging the da- ta; determining a first experimental performance parameter (P2) in the first predetermined time span and a second exper- imental performance parameter (P3) in the second predeter- mined time span from the averaged data for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direction; calculating an experimental performance parameter dif- ference (P3 – P2) between the first and second experimental performance parameters (P3, P2) for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direc- tion; determining a first wind direction (WD2) in the first predetermined time span and a second wind direction (WD3) in the second predetermined time span from the averaged data for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direction; calculating a first theoretical performance parameter in the first predetermined time span based on the determined first wind direction (WD2) and a second theoretical perfor- mance parameter in the second predetermined time span based on the determined second wind direction (WD3) for each yaw operation in the clockwise yaw direction and the counter- clockwise yaw direction; calculating a theoretical performance parameter differ- ence between the first and second theoretical performance pa- rameters for each yaw operation in the clockwise yaw direc- tion and the counter-clockwise yaw direction; calculating absolute errors (E_{cw + ccw}) between the exper- imental performance parameter difference and the theoretical performance parameter difference of the yaw operations in the clockwise direction and a counter-clockwise direction, re- spectively; adding the absolute errors (Ecw, Eccw) of the yaw opera- tions in the clockwise direction and the counter-clockwise direction to obtain a total error (Ecw + Eccw); determining a minimum error (idx) of the total error (Ecw + Eccw); and determining a yaw misalignment (γ) based on the minimum error (idx).

2. The method according to the preceding claim, further comprising steps of: performing a yaw event at a yaw event time (T0) in the clockwise direction and the counter-clockwise direction, re- spectively; selecting a predetermined further time span directly be- fore the yaw event time (T0) for each yaw event in the clock- wise direction and the counter-clockwise direction; recording data of a wind direction and a performance pa- rameter in the predetermined further time span before the yaw event time (T0), and averaging the data for each yaw event in the clockwise direction and the counter-clockwise direction; determining a further first experimental performance pa- rameter (P1) at the beginning of the further time span and a further second experimental performance parameter (P2) at the end of the further time span from the averaged data for each yaw event in the clockwise direction and the counter- clockwise direction; calculating a further experimental performance parameter difference (P2 - P1) between the further first and further second experimental performance parameters (P1, P2) for each yaw event in the clockwise direction and the counter- clockwise direction; determining a further first wind direction (WD1) at the beginning of the further time span and a further second wind direction (WD2) at the end of the further time span from the averaged data for each yaw event in the clockwise direction and the counter-clockwise direction; calculating a further first theoretical performance pa- rameter (Pγ+WD1) at the beginning of the further time span based on the determined further first wind direction (WD1) and a further second theoretical performance parameter (Pγ+WD2) at the end of the further time span based on the de- termined further second wind direction (WD2) for each yaw event in the clockwise direction and the counter-clockwise direction; calculating a further theoretical performance parameter difference (Pγ+WD1 - Pγ+WD2) between the further first and second theoretical performance parameters (Pγ+WD1, Pγ+WD2) for each yaw event in the clockwise direction and the coun- ter-clockwise direction; calculating further absolute errors (Ecw, Eccw) between the further experimental performance parameter difference (P2 - P1) and the further theoretical performance parameter dif- ference (Pγ+WD1 - Pγ+WD2) of the yaw events in the clockwise direction and the counter-clockwise direction, respectively; adding the further absolute errors (Ecw, Eccw) of the yaw events in the clockwise direction and the counter- clockwise direction to obtain a further total error (Ecw + Eccw); determining a further minimum (idx) of the further total error; and determining a further yaw misalignment based on the fur- ther minimum error.

3. The method according to claim 2, wherein the steps of claim 2 are performed after the steps of claim 1.

4. The method according to any one of the preceding claims, wherein the yaw operation moves the nacelle in a range between -4° and +4°, preferably in a range between -3° and +3°, more preferred in a range between -2° and +2°.

5. The method according to any one of the preceding claims, wherein averaging the data includes a filtering the data.

6. The method according to any one of the preceding claims, wherein the predetermined time span is in a range between 30 and 240 s, preferably between 60 and 180 s.

7. The method according to any one of the preceding claims, wherein the yaw misalignment is determined in a matrix which in- cludes the error and the yaw misalignment for a range of wind direction offsets and yaw loss exponents.

8. The method according to any one of the preceding claims, wherein the first wind direction (WD2) is determined by use of a wind sensor, wherein sampled wind direction values are aver- aged at least in a part of the first predetermined time span; and/or the second wind direction (WD3) is determined by use of a wind sensor, wherein sampled wind direction values are av- eraged at least in a part of the second predetermined time span.

9. The method according to any one of the preceding claims, wherein the first theoretical performance parameter Pγ+WD2 is calculated as Pγ+WD2 = cos^∞(γ + WD2); and/or the second theoretical performance parameter Pγ+WD3 is calculated as Pγ+WD3 = cos^∞(γ + WD3); wherein α is a yaw loss exponent and γ is the yaw misa- lignment.

10. The method according to any one of the preceding claims, wherein the error (Ecw + Eccw) is calculated as a sum of a first absolute error (Ecw) of the yaw operation in the clockwise yaw direction and a second absolute error (Eccw) of the yaw operation in the counter-clockwise yaw direction.

11. The method according to any one of the preceding claims, wherein the performance parameter is selected from a group com- prising a power-based parameter of an active electrical or mechanical output power of the wind turbine (1), and a wind speed-based parameter of an effective wind speed.

12. A device of calibrating a yaw system of a wind turbine, the wind turbine (1) comprising a rotor (4) having a plurali- ty of rotor blades (6), each blade (6) being configured to be pitched by a pitch angle about a pitch axis of the blade (6), the rotor (4) being mounted to a nacelle (3) to rotate about a rotation axis (8) with a rotor speed to drive a generator (5) for producing electrical energy, the nacelle (3) being mounted to a tower (2) to rotate about a yaw axis (9), the device comprising: a selecting unit for selecting a first predetermined time span before a yaw operation and a second predetermined time span after the yaw operation; a performing unit for performing a yaw operation in a clockwise yaw direction and a yaw operation in a counter- clockwise yaw direction; a recording unit for recording data of a wind direction and a performance parameter caused by both yaw operations, and averaging the data; a first determining unit for determining a first experi- mental performance parameter (P2) in the first predetermined time span and a second experimental performance parameter (P3) in the second predetermined time span from the averaged data for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direction; a first calculating unit for calculating an experimental performance parameter difference (P3 – P2) between the first and second experimental performance parameters (P3, P2) for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direction; a second determining unit for determining a first wind direction (WD2) in the first predetermined time span and a second wind direction (WD3) in the second predetermined time span from the averaged data for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw direc- tion; a second calculating unit for calculating a first theo- retical performance parameter in the first predetermined time span based on the deter-mined first wind direction (WD2) and a second theoretical performance parameter in the second pre- determined time span based on the determined second wind di- rection (WD3) for each yaw operation in the clockwise yaw di- rection and the counter-clockwise yaw direction; a third calculating unit for calculating a theoretical performance parameter difference between the first and second theoretical performance parameters for each yaw operation in the clockwise yaw direction and the counter-clockwise yaw di- rection; a fourth calculating unit for calculating absolute er- rors (Ecw, Eccw) between the experimental performance parame- ter difference and the theoretical performance parameter dif- ference of the yaw operations in the clockwise direction and a counter-clockwise direction, respectively; an adding unit configured to add the absolute errors (Ecw, Eccw) of the yaw operations in the clockwise direction and the counter-clockwise direction to obtain a total error (Ecw + Eccw); a third determining unit for determining a minimum error (idx) of the total error (Ecw + Eccw); and a fourth determining unit for determining a yaw misa- lignment (γ) based on the minimum error (idx).